Answer:
[tex] \sqrt{160} [/tex]
Step-by-step explanation:
Te equation of line is:
y = 3x + 12
Plug x = 0 in the above equation of line, we find:
y = 3*0 + 12
y = 0 + 12
y = 12
y-intercept = (0, 12)
Plug y = 0 in the equation y = 3x + 12
0 = 3x + 12
-3x = 12
x = 12/(-3)
x = - 4
x-intercept = (-4, 0)
Distance between x-intercept and y--intercept
[tex] = \sqrt{ {( - 4 - 0)}^{2} + {(0 - 12)}^{2} } \\ \\ = \sqrt{ {( - 4 )}^{2} + {(- 12)}^{2} } \\ \\ = \sqrt{16 + 144} \\ \\ = \sqrt{160} [/tex]
